The shell structures of the Baroque

The shell s uc u es o he Ba oque F. ~sc i~', V. ~o n~h', J. ~jnchez' & J. P. ~alc i cel~ Uni e si y o Se ille, Spain 2 P o esso o S uc u es o he Uni e si y o LaCo uiia, Spain Abs ac The Ba oque has been adi ionally a s yle minimized by i s endency o deco a ion and i s lack o he sys ema ic. G adually i has le demons a ing ha his was a p ejudice and ha he a chi ec u al alues we e o i s magni ude, compa able o he bigges landma ks o classic s yles. As o he s uc u al aspec s we wan o demons a e ha hey o e come o as much as i was made p e iously by hei space weal h, hei economy o means and he in elligence o hei solu ions. Somehow hey ep esen an an eceden o he shell a chi ec u e ha so much i would make an exhibi ion wi h he Rein o ced Conc e e and he analy ic echniques o dimensioning. Wi h less means bu wi h g ea in ui ion, he Ba oque, in en ed o ms o a complexi y ha oday is s ill di icul o unde s and, a leas geome ically. Pa adoxically he e a e no in es iga ions ha help us o cla i y he s uc u al mi acle o he Ba oque since up o now i has been in his o ians' hands and no hose o a chi ec s o enginee s. This a icle ies o open he oad in his unexplo ed ield. 1. In oduc ion To speak o shell s uc u es in he ma hema ical and modem sense o he e m, in designs p e ious o 1900 and in ma e ials di e en o he ein o ced conc e e i seems an excessi e license. Howe e , since in he XIX cen u y he b ick aul s al eady demons a ed a good capaci y o adop cap icious o ms in absence o lexions and wi h he b ick and he mo a like only ma e ials. I is logical o hink ha he cons uc ion o his shells is p e ious o hei analy ic ools, so p e ious jus i ica ion ha i can be ex apola ed o he Byzan ine cons uc ion in ha chu ches like Se lio and Bacchus o S a. So ia, hey ha e been able o be designed like memb anes, wi h g ea p ecision i we compa e hem wi h he esul s ob ained by Fini e Elemen s. Howe e he i s p ope ly shells a e no ound un il he Ba oque a chi ec u e, and no in ac in he I alian whe e a chi ec s like B unelleschi, Miguel ~n~el o Palladio did g ea achie emen s o o e come he s uc u al challenges o he T ansac ions on he Buil En i onmen ol 66, © 2003 WIT P ess, www.wi p ess.com, ISSN 1743-3509 66 S cc al S udi ~, R pam a d Ma n o anc o H i ag Aldzi c uw V111 an iqui y. I is la e , when he economy o means ha he XVIII Cen u y imposed o he cons uc ion, when a g ea quan i y o app en ices, ha we e o med in San Ped o's ac o y, we e dissemina ed by Eu ope o c ea e some na ional s yles, ich in way, splendid o concep and good s uc u ally. 2. The Ba oque s uc u es The new gene a ion ha was in I aly, ollowing Miguel Angelo and Bo omini guidelines, p e e ed o ma e ialize hei s uc u es in ne es and complex laces e y o he medie al s yle. Gua ini (Fig. 1) o Vi one (Fig. 2) hey go in his line. Fig. l. S . Lau ence in Tu in by Gua ino Gua ini Fig.2. S . Be na dino in Chie i by Vi one Fig.3. S . Cha les in Vienna Fische on E lach. Who mo ed o he no h hey p e e ed o s ill use con inuous o ms mo e complex han he men ioned ne es, al hough masked unde a dense o namen al laye o s uccos and pain ings. Fische on E lach, pa ia ch o all hem, in Aus ia, he amily Dien zenho e in P ague and Neuman in Ge many a e some ew ones o among he dozens o a ch ec s ha we could men ion ha , wi h i s di e ences hey dehca ed o c ea e sugges i e and complex spaces wi h minimum s uc u es. Fig. 4. Selec ion pa s o a sphe e o build he aul s by Geo ge Dien zenho e . T ansac ions on he Buil En i onmen ol 66, © 2003 WIT P ess, www.wi p ess.com, ISSN 1743-3509 While Fische was de o ed o explo e he ellip ic spaces (Fig.3) and he Dien zenho e amily he in e sec ed geome ies (Fig. 4), Neuman manages wi h ease he mos di icul spaces, mix u e o ellipsoids and cylinde s on punc ual suppo s (Fig. 5). Zimme man ge s geome ies ha don' ha e ecognisable o ms (Fig, 6). Fig. 5. Type o Neuman Cons uc ion. Fig.6. Zimme man's S einhausen Chu ch. When we begun he s udy on he s uc u es o he Ba oque, we we e su p ised by he lack o bibliog aphy and o speci ic s udies. I is accen ua ed i in he case o he Cen al Eu opean Ba oque, in he which, apa analysis made o consolida ion wo ks and epai o econs uc ion, doesn' exis p ac ically any esea ch. We excep Jage and C oci al hough hey ha e no in e ened in pa icula aspec s o shells. I is o i ha we con ibu e he da a ha con inue wi h in en ion o o open he oad and o demons a e he g ea s uc u al in e es ha has a ecen ly alued s yle. The wo k is wide and i will emb ace he di e en ypes o Ba oque memb ane. Bu a his ime i is logical o begin wi h impo an and e y well- known monumen s, like hey can be: Fig.7. Sanc ua y o Kappel. Fig.8.Chu ch o Vie zhenheiling.Fig. 9. Ne esheim. T ansac ions on he Buil En i onmen ol 66, © 2003 WIT P ess, www.wi p ess.com, ISSN 1743-3509 68 S cc al S udi ~, R pam a d Ma n o anc o H i ag Aldzi c uw V111 1) Sanc ua y o Kappel nea Waldhsassen o Geo ge Dienzenho e (Fig. 7). 2) Chu ch o pilg image o S einhausen o Zim ne man (Fig. 6). 3) F anciscan chu ch o Ve zhenheiling, by Neuman (Fig. 8). 4) Benedic ine chu ch o Ne esheim, by Neuman (Fig. 9) In all hese cases we will make he same supposi ions: a) Fo lack o da a we conside ha he aul s a e buil wi h b icks o h ead and he e o e wi h a hickness o 0.25 m. b) The cha ac e is ics o he ab ic a e he ollowing ones: 1. y=1.7~on/m~ 2. E = 10 E~ ~on/m~ and he ma e ial is elas ic and lineal in he conside ed ange. 3. U = 116 c) The aul s a e suppo ed by hinges on he co nices and only he pa upon hem a e calcula ed s a ing om his le el. I is necessa y o keep in mind ha he co nices, in he Ba oque, de ine he o m in plan and ha wha he e a e unde hem is well es ed. d) The only ac ions ha we will conside hey a e hose o own weigh . e) The ma hema ical pa e n ha we will use is o conside he medium su ace o he aul as he geome y o analysis. ) The me hod used o calcula ion is ha o Fini e Elemen s. The esul ing g aphics will ep esen he e o s and displacemen s in he conside ed su ace. 3. Sanc ua y o Kappel in Waldsassen: by Geo ge Dien zenho e In his case we ha e a es ange unc ional dis ibu ion wi h a iangula plan wi h cu ed sides, acco ding o he geome ic ou line o he Fig. 7. I has odd numbe o sides, wi h solid walls pe o a ed wi h chapels and s abilizing owe s. The dome is o med by a sphe e ha in e sec s wi h o he h ee, and he g oup is suppo ed in all i s con ou . The e a e no mo e pe o a ions han some small chimneys ha p o ide a so cla i y (Fig. 10). Fig. 10. In e io o he Sanc ua y o Kappel. Fig. 1 1. Scheme o de lec ions. T ansac ions on he Buil En i onmen ol 66, © 2003 WIT P ess, www.wi p ess.com, ISSN 1743-3509 I we calcula e in elas ic condi ion we see: a) The maximum de lec ions a e, in h~s case, o 4.5 mm. (Fig. 11) b) The maximum momen s a e o 0.32 Tonxm in a punc ual case ha is es ed by he owe s, ha ha e no been conside ed in he calcula ion in he p ac ice. In gene al, in signi ican a eas he maximum momen s a e o 50% o his alue (Fig. 12). Fig. 12 Scheme o bending momen s. Fig. 13 P incipal s esses I c) The maximum ensions a e, in gene al, smalle han 13 onlm2, al hough, locally, in a eas ha in ac go ein o ced and ha we ha e no conside ed hey a i e o 82 ~on/m~ (Figs. 13). This co e , o g ea size and o m, misses i is ex ao dina ily e ec i e whene e hey s ay i s ein o cemen ne es. 4. Chu ch o pilg image o S einhausen: by Nicholas Zimme man The used geome ic pa e n is an ellipsoid upon en suppo s (Fig. 6). I we calcula e in elas ic s a e, we ob ain he ollowing conclusions: a) The maximum de lec ions a e o 0.226 mm. o own weigh (Fig. 14). Fig. 14 De lec ions Fig. 15. Bending Momen s. X axis. b) As o he maximum momen s, excep o due punc ual a eas o he g id o he ma hema ical pa e n, he maxima a e o 0.13 Tonxm. in he a ea among cylind ical openings (Fig. 15) o o 0.3 Tonxm. in he same T ansac ions on he Buil En i onmen ol 66, © 2003 WIT P ess, www.wi p ess.com, ISSN 1743-3509 70 S cc al S udi ~, R pam a d Ma n o anc o H i ag Aldzi c uw V111 pe o a ions ein o cemen . This is alse in ou case since hey ha e a eas specially ein o ced by o namen al elemen s. (Fig. 16). Fig. 16. Dome o he S einhausen chu ch Fig. l7 and 18 P incipal s esses. c) As o he ension s esses, you lea e in he Figs. 17 and 18 ha he 9 Ton/m2 doesn' su passed in any poin . On he whole i means i ha i s ops own weigh and s a ic loads gi e a sa e s a e. This s uc u e canno ha e pa hology and i s design is good. 5. F anciscan Chu ch o Vie zhenheiling: by Bal hasa Neuman The geome y is ex emely complex and he aul is o med by he in e sec ion o h ee ellipsoids, wo sphe es, wo cylinde s and wen y- wo cylind ical openings, in such a way ha he whole g oup suppo s on wen y- ou poin s (Fig. 8). All he in e sec ions and bo de s a e conside ed mished o by ne es o 0.5x0.5 m. (Fig. 19 and 20). The analysis e eals beha iou as a shell wi h e y good esul s ha app oaches o he memb ane s a e, wi h he excep ion o some poin s. a) In he Fig. 21 a e app ecia ed he displace nen s ha , in he wo s in he cases, hey don' o e come he 0 .7 mm. in he key o he in e sec ion cylinde s. b) As o he ension s esses we ha e a widesp ead s a e ha i oscilla es be ween 3 and -3 Tonlm2. In he in e sec ion ne es we e en ha e 30 ~on/m' o ac ion s esses (Fig. 22). Fo comp ession s esses, in he kidneys o he domes, i a i es o 30 Ton/m2 (Fig. 23). T ansac ions on he Buil En i onmen ol 66, © 2003 WIT P ess, www.wi p ess.com, ISSN 1743-3509 Fig. 19. D awing o a longi udinal sec ion. Fig. 20. In e nal iew o he shell Fig 2 1. Scheme o displacemen s. c) Fo he bending momen s hey oscilla e among +/-0.15 Tonxm in he X di ec ion (Fig. 24). Some hing g ea es a e in he ne es in he Y di ec ion (Fig. 25), al hough inside he accep able ange. Fig. 22. P incipal Tension s esses I Fig. 23. P incipal ension s esses 11. T ansac ions on he Buil En i onmen ol 66, © 2003 WIT P ess, www.wi p ess.com, ISSN 1743-3509 72 S cc al S udi ~, R pam a d Ma n o anc o H i ag Aldzi c uw V111 Fig. 24. Bending Momen s X Fig. 25. Bending Momen s Y 6. Benedic ine Chu ch o Ne esheim: by Bal asa Neuman The a chi ec u e o his chu ch is ex emely complex and i is one in he mos complica ed mas e piece in he whole Ba oque (Fig. 9). He e we ha e he in e sec ion o se en ellipsoids o di e en size and heigh wi h sphe ical canyons, in acco dance wi h he geome y o he Fig. 26. The whole is su p ising (Fig. 27). The s uc u al beha iou o he g oup is deduced om he calcula ion by means o Fini e Elemen s wi h he ollowing esul s: Fig. 26 Longi udinal sec ion o he Ne esheim Chu ch. a) In he Fig. 28 a e app ecia ed he displacemen s ha , in he wo s in he cases, hey don' o e come he 16 mm. in he key o he in e sec ion cylinde s. b) As o he ension s esses we ha e a widesp ead s a e ha i oscilla es be ween -9 and 3 ~onlm~. In he penden i s we e en ha e 60 ~on n' o ac ion s esses (Fig. 29 and 30). c) Fo he bending momen s hey oscilla e among +/-0.20 Tonxm in he X di ec ion (Fig. 3 1). Some hing g ea es a e in he ne es in he Y di ec ion (Fig. 32), al hough inside he accep able ange. (0.50 Tonxm.). T ansac ions on he Buil En i onmen ol 66, © 2003 WIT P ess, www.wi p ess.com, ISSN 1743-3509 Fig. 27 In e nal iew o he Ne esheim aul s. NODAL SOLUI ON Fig. 28. De lec ions scheme. 7. Conclusions Al hough i is di icul o es ablish some conclusions a he p esen s a e o he esea ch we wan poin on he in e es o his kind o cons uc ion so li le s udied and so in e es ing. Ou in e es is o ex end he s udy o all he Ba oque p oposals ha a e so di e en ia ed o o he s yles, de eloped be o e o a e . Fig. 29. P incipal es eses I Fig. 30. P incipal es eses I1 T ansac ions on he Buil En i onmen ol 66, © 2003 WIT P ess, www.wi p ess.com, ISSN 1743-3509